The grades on a history midterm at Oak are normally distributed with $\mu = 67$ and $\sigma = 5.5$. Ashley earned a $77$ on the exam. Find the z-score for Ashley's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ashley's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{77 - {67}}{{5.5}}} $ ${ z \approx 1.82}$ The z-score is $1.82$. In other words, Ashley's score was $1.82$ standard deviations above the mean.